I recently had to give one of mine the same med and even though I have decades of experience giving injections to humans, I hated and was nervous about giving them to my cham. I found that taking him out of his enclosure for it was the worst for the both of us. So, I left him in his enclosure...
Your guy should be okay. It’s possible that she didn’t truly drop him, but that he may have become overly stressed and threw himself to the floor as a last ditch attempt to escape the giant predator. Chameleons will do this when in trees and while it freaks us out, they are usually just fine.
In case of prolapse, soaking in a sugar water helps to shrink the prolapsed tissues. While prolapses aren’t a terribly common occurrence, it’s not a bad addition to have in a first aid kit. I’m surprised by the number of homes I’ve been in where they don’t have sugar.
I’m not sure how you would plan for a tornado or power outage , since those are random surprise events. However, some keep a ‘bug out’ bag at the ready in case of needing to move your chameleon for evacuation. A mesh pop up hamper with zipper closure makes for a convenient emergency enclosure...